arXiv subjects

Hanzhong Liu

Publications and source records attributed to Hanzhong Liu.

At least 19 recordsLinked to original sources

arXiv2026

Design-based edge-level causal inference with machine learning assisted covariate adjustment

We study design-based causal inference for edge-level outcomes in directed networks under dyadic interference. In this setting, outcomes are defined on directed edges and depend on the joint treatment assignments of pairs of units, inducing a complex dependence structure that invalidates standard estimation and inference procedures developed for node-level data. We construct Horvitz--Thompson estimators for a general class of edge-level causal effects and establish their asymptotic normality under mild regularity conditions. To enable valid inference, we develop variance estimators that exploit identifiable components of network dependence, yielding substantially less conservative bounds than classical approaches. To improve efficiency, we incorporate auxiliary covariates through a sample splitting and cross-fitting procedure. A key technical challenge is that standard two-fold sample splitting fails in the presence of edge-level outcomes due to the dependence induced by shared units. To address this issue, we introduce a three-fold sample splitting and cross-fitting scheme that restores the conditional independence required for unbiased estimation. Under a stability condition, the resulting covariate-adjusted estimator is asymptotically normal and accommodates both linear adjustment and flexible machine learning methods. We further introduce a calibration step that guarantees no asymptotic efficiency loss relative to the unadjusted estimator. Simulation studies and a real-data application confirm the theoretical results and demonstrate substantial efficiency gains.

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arXiv2025

Design-based theory for causal inference

Causal inference, as a major research area in statistics and data science, plays a central role across diverse fields such as medicine, economics, education, and the social sciences. Design-based causal inference begins with randomized experiments and emphasizes conducting statistical inference by leveraging the known randomization mechanism, thereby enabling identification and estimation of causal effects under weak model dependence. Grounded in the seminal works of Fisher and Neyman, this paradigm has evolved to include various design strategies, such as stratified randomization and rerandomization, and analytical methods including Fisher randomization tests, Neyman-style asymptotic inference, and regression adjustment. In recent years, with the emergence of complex settings involving high-dimensional data, individual noncompliance, and network interference, design-based causal inference has witnessed remarkable theoretical and methodological advances. This paper provides a systematic review of recent progress in this field, focusing on covariate-balanced randomization designs, design-based statistical inference methods, and their extensions to high-dimensional, noncompliance, and network interference scenarios. It concludes with a comprehensive perspective on future directions for the theoretical development and practical applications of causal inference.

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arXiv2025

From Generic to Specialized: A Subspecialty Diagnostic System Powered by Self-Supervised Learning for Cervical Histopathology

Cervical cancer remains a major malignancy, necessitating extensive and complex histopathological assessments and comprehensive support tools. Although deep learning shows promise, these models still lack accuracy and generalizability. General foundation models offer a broader reach but remain limited in capturing subspecialty-specific features and task adaptability. We introduce the Cervical Subspecialty Pathology (CerS-Path) diagnostic system, developed through two synergistic pretraining stages: self-supervised learning on approximately 190 million tissue patches from 140,000 slides to build a cervical-specific feature extractor, and multimodal enhancement with 2.5 million image-text pairs, followed by integration with multiple downstream diagnostic functions. Supporting eight diagnostic functions, including rare cancer classification and multimodal Q&A, CerS-Path surpasses prior foundation models in scope and clinical applicability. Comprehensive evaluations demonstrate a significant advance in cervical pathology, with prospective testing on 3,173 cases across five centers maintaining 99.38% screening sensitivity and excellent generalizability, highlighting its potential for subspecialty diagnostic translation and cervical cancer screening.

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arXiv2025

Conditional cross-fitting for unbiased machine-learning-assisted covariate adjustment in randomized experiments

Randomized experiments are the gold standard for estimating the average treatment effect (ATE). While covariate adjustment can reduce the asymptotic variances of the unbiased Horvitz-Thompson estimators for the ATE, it suffers from finite-sample biases due to data reuse in both prediction and estimation. Traditional sample-splitting and cross-fitting methods can address the problem of data reuse and obtain unbiased estimators. However, they require that the data are independently and identically distributed, which is usually violated under the design-based inference framework for randomized experiments. To address this challenge, we propose a novel conditional cross-fitting method, under the design-based inference framework, where potential outcomes and covariates are fixed and the randomization is the sole source of randomness. We propose sample-splitting algorithms for various randomized experiments, including Bernoulli randomized experiments, completely randomized experiments, and stratified randomized experiments. Based on the proposed algorithms, we construct unbiased covariate-adjusted ATE estimators and propose valid inference procedures. Our methods can accommodate flexible machine-learning-assisted covariate adjustments and allow for model misspecification.

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arXiv2025

Regression adjustment in covariate-adaptive randomized experiments with missing covariates

Covariate-adaptive randomization is widely used in clinical trials to balance prognostic factors, and regression adjustments are often adopted to further enhance the estimation and inference efficiency. In practice, the covariates may contain missing values. Various methods have been proposed to handle the covariate missing problem under simple randomization. However, the statistical properties of the resulting average treatment effect estimators under stratified randomization, or more generally, covariate-adaptive randomization, remain unclear. To address this issue, we investigate the asymptotic properties of several average treatment effect estimators obtained by combining commonly used missingness processing procedures and regression adjustment methods. Moreover, we derive consistent variance estimators to enable valid inferences. Finally, we conduct a numerical study to evaluate the finite-sample performance of the considered estimators under various sample sizes and numbers of covariates and provide recommendations accordingly. Our analysis is model-free, meaning that the conclusions remain asymptotically valid even in cases of misspecification of the regression model.

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arXiv2025

Rejoinder to Reader Reaction "On exact randomization-based covariate-adjusted confidence intervals" by Jacob Fiksel

We applaud Fiksel (2024) for their valuable contributions to randomization-based inference, particularly their work on inverting the Fisher randomization test (FRT) to construct confidence intervals using the covariate-adjusted test statistic. FRT is advocated by many scholars because it produces finite-sample exact p-values for any test statistic and can be easily adopted for any experimental design (Rosenberger et al., 2019; Proschan and Dodd, 2019; Young, 2019; Bind and Rubin, 2020). By inverting FRTs, we can construct the randomization-based confidence interval (RBCI). To the best of our knowledge, Zhu and Liu (2023) are the first to analytically invert the FRT for the difference-in-means statistic. Fiksel (2024) extended this analytical approach to the covariate-adjusted statistic, producing a monotonic p-value function under certain conditions. In this rejoinder, we propose an analytical approach to invert the FRT for test statistics that yield a non-monotonic p-value function, with the studentized t-statistic as an important special case. Exploiting our analytical approach, we can recover the non-monotonic p-value function and construct RBCI based on the studentized t-statistic. The RBCI generated by the proposed analytical approach is guaranteed to achieve the desired coverage probability and resolve the contradiction between Luo et al. (2021) and Wu and Ding (2021). Simulation results validate our findings and demonstrate that our method is also computationally efficient.

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arXiv2025

Minimax Optimal Design with Spillover and Carryover Effects

In various applications, the potential outcome of a unit may be influenced by the treatments received by other units, a phenomenon known as interference, as well as by prior treatments, referred to as carryover effects. These phenomena violate the stable unit treatment value assumption and pose significant challenges in causal inference. To address these complexities, we propose a minimax optimal experimental design that simultaneously accounts for both spillover and carryover effects, enhancing the precision of estimates for direct and spillover effects. This method is particularly applicable to multi-unit experiments, reducing sample size requirements and experimental costs. We also investigate the asymptotic properties of the Horvitz--Thompson estimators of direct and spillover effects, demonstrating their consistency and asymptotic normality under the minimax optimal design. To facilitate valid inferences, we propose conservative variance estimators. Furthermore, we tackle the challenges associated with potential misspecifications in the order of carryover effects. Our approach is validated by comprehensive numerical studies that demonstrate superior performance compared to existing experimental designs.

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arXiv2024

Imputation-based randomization tests for randomized experiments with interference

The presence of interference renders classic Fisher randomization tests infeasible due to nuisance unknowns. To address this issue, we propose imputing the nuisance unknowns and computing Fisher randomization p-values multiple times, then averaging them. We term this approach the imputation-based randomization test and provide theoretical results on its asymptotic validity. Our method leverages the merits of randomization and the flexibility of the Bayesian framework: for multiple imputations, we can either employ the empirical distribution of observed outcomes to achieve robustness against model mis-specification or utilize a parametric model to incorporate prior information. Simulation results demonstrate that our method effectively controls the type I error rate and significantly enhances the testing power compared to existing randomization tests for randomized experiments with interference. We apply our method to a two-round randomized experiment with multiple treatments and one-way interference, where existing randomization tests exhibit limited power.

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arXiv2024

Incorporating external data for analyzing randomized clinical trials: A transfer learning approach

Randomized clinical trials are the gold standard for analyzing treatment effects, but high costs and ethical concerns can limit recruitment, potentially leading to invalid inferences. Incorporating external trial data with similar characteristics into the analysis using transfer learning appears promising for addressing these issues. In this paper, we present a formal framework for applying transfer learning to the analysis of clinical trials, considering three key perspectives: transfer algorithm, theoretical foundation, and inference method. For the algorithm, we adopt a parameter-based transfer learning approach to enhance the lasso-adjusted stratum-specific estimator developed for estimating treatment effects. A key component in constructing the transfer learning estimator is deriving the regression coefficient estimates within each stratum, accounting for the bias between source and target data. To provide a theoretical foundation, we derive the $l_1$ convergence rate for the estimated regression coefficients and establish the asymptotic normality of the transfer learning estimator. Our results show that when external trial data resembles current trial data, the sample size requirements can be reduced compared to using only the current trial data. Finally, we propose a consistent nonparametric variance estimator to facilitate inference. Numerical studies demonstrate the effectiveness and robustness of our proposed estimator across various scenarios.

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arXiv2024

Estimation and inference of average treatment effects under heterogeneous additive treatment effect model

Randomized experiments are the gold standard for estimating treatment effects, yet network interference challenges the validity of traditional estimators by violating the stable unit treatment value assumption and introducing bias. While cluster randomized experiments mitigate this bias, they encounter limitations in handling network complexity and fail to distinguish between direct and indirect effects. To address these challenges, we develop a design-based asymptotic theory for the existing Horvitz--Thompson estimators of the direct, indirect, and global average treatment effects under Bernoulli trials. We assume the heterogeneous additive treatment effect model with a hidden network that drives interference. Observing that these estimators are inconsistent in dense networks, we introduce novel eigenvector-based regression adjustment estimators to ensure consistency. We establish the asymptotic normality of the proposed estimators and provide conservative variance estimators under the design-based inference framework, offering robust conclusions independent of the underlying stochastic processes of the network and model parameters. Our method's adaptability is demonstrated across various interference structures, including partial interference and local interference in a two-sided marketplace. Numerical studies further illustrate the efficacy of the proposed estimators, offering practical insights into handling network interference.

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arXiv2024

Treatment effect estimation under covariate-adaptive randomization with heavy-tailed outcomes

Randomized experiments are the gold standard for investigating causal relationships, with comparisons of potential outcomes under different treatment groups used to estimate treatment effects. However, outcomes with heavy-tailed distributions pose significant challenges to traditional statistical approaches. While recent studies have explored these issues under simple randomization, their application in more complex randomization designs, such as stratified randomization or covariate-adaptive randomization, has not been adequately addressed. To fill the gap, this paper examines the properties of the estimated influence function-based M-estimator under covariate-adaptive randomization with heavy-tailed outcomes, demonstrating its consistency and asymptotic normality. Yet, the existing variance estimator tends to overestimate the asymptotic variance, especially under more balanced designs, and lacks universal applicability across randomization methods. To remedy this, we introduce a novel stratified transformed difference-in-means estimator to enhance efficiency and propose a universally applicable variance estimator to facilitate valid inferences. Additionally, we establish the consistency of kernel-based density estimation in the context of covariate-adaptive randomization. Numerical results demonstrate the effectiveness of the proposed methods in finite samples.

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arXiv2024

Inference under covariate-adaptive randomization with many strata

Covariate-adaptive randomization is widely employed to balance baseline covariates in interventional studies such as clinical trials and experiments in development economics. Recent years have witnessed substantial progress in inference under covariate-adaptive randomization with a fixed number of strata. However, concerns have been raised about the impact of a large number of strata on its design and analysis, which is a common scenario in practice, such as in multicenter randomized clinical trials. In this paper, we propose a general framework for inference under covariate-adaptive randomization, which extends the seminal works of Bugni et al. (2018, 2019) by allowing for a diverging number of strata. Furthermore, we introduce a novel weighted regression adjustment that ensures efficiency improvement. On top of establishing the asymptotic theory, practical algorithms for handling situations involving an extremely large number of strata are also developed. Moreover, by linking design balance and inference robustness, we highlight the advantages of stratified block randomization, which enforces better covariate balance within strata compared to simple randomization. This paper offers a comprehensive landscape of inference under covariate-adaptive randomization, spanning from fixed to diverging to extremely large numbers of strata.

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arXiv2024

Sharp variance estimator and causal bootstrap in stratified randomized experiments

Randomized experiments are the gold standard for estimating treatment effects, and randomization serves as a reasoned basis for inference. In widely used stratified randomized experiments, randomization-based finite-population asymptotic theory enables valid inference for the average treatment effect, relying on normal approximation and a Neyman-type conservative variance estimator. However, when the sample size is small or the outcomes are skewed, the Neyman-type variance estimator may become overly conservative, and the normal approximation can fail. To address these issues, we propose a sharp variance estimator and two causal bootstrap methods to more accurately approximate the sampling distribution of the weighted difference-in-means estimator in stratified randomized experiments. The first causal bootstrap procedure is based on rank-preserving imputation and we prove its second-order refinement over normal approximation. The second causal bootstrap procedure is based on constant-treatment-effect imputation and is further applicable in paired experiments. In contrast to traditional bootstrap methods, where randomness originates from hypothetical super-population sampling, our analysis for the proposed causal bootstrap is randomization-based, relying solely on the randomness of treatment assignment in randomized experiments. Numerical studies and two real data applications demonstrate advantages of our proposed methods in finite samples. The \texttt{R} package \texttt{CausalBootstrap} implementing our method is publicly available.

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arXiv2023

A unified framework for covariate adjustment under stratified randomization

Randomization, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomized experiments, the treatment effect is a parameter of general interest. Researchers have explored the validity of using linear models to estimate the treatment effect and perform covariate adjustment and thus improve the estimation efficiency. However, the relationship between covariates and outcomes is not necessarily linear, and is often intricate. Advances in statistical theory and related computer technology allow us to use nonparametric and machine learning methods to better estimate the relationship between covariates and outcomes and thus obtain further efficiency gains. However, theoretical studies on how to draw valid inferences when using nonparametric and machine learning methods under stratified randomization are yet to be conducted. In this paper, we discuss a unified framework for covariate adjustment and corresponding statistical inference under stratified randomization and present a detailed proof of the validity of using local linear kernel-weighted least squares regression for covariate adjustment in treatment effect estimators as a special case. In the case of high-dimensional data, we additionally propose an algorithm for statistical inference using machine learning methods under stratified randomization, which makes use of sample splitting to alleviate the requirements on the asymptotic properties of machine learning methods. Finally, we compare the performances of treatment effect estimators using different machine learning methods by considering various data generation scenarios, to guide practical research.

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arXiv2023

A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effect

Interpretability plays a crucial role in the application of statistical learning to estimate heterogeneous treatment effects (HTE) in complex diseases. In this study, we leverage a rule-based workflow, namely causal rule learning (CRL), to estimate and improve our understanding of HTE for atrial septal defect, addressing an overlooked question in the previous literature: what if an individual simultaneously belongs to multiple groups with different average treatment effects? The CRL process consists of three steps: rule discovery, which generates a set of causal rules with corresponding subgroup average treatment effects; rule selection, which identifies a subset of these rules to deconstruct individual-level treatment effects as a linear combination of subgroup-level effects; and rule analysis, which presents a detailed procedure for further analyzing each selected rule from multiple perspectives to identify the most promising rules for validation. Extensive simulation studies and real-world data analysis demonstrate that CRL outperforms other methods in providing interpretable estimates of HTE, especially when dealing with complex ground truth and sufficient sample sizes.

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arXiv2022

Tyranny-of-the-minority regression adjustment in randomized experiments

Regression adjustment is widely used for the analysis of randomized experiments to improve the estimation efficiency of the treatment effect. This paper reexamines a weighted regression adjustment method termed as tyranny-of-the-minority (ToM), wherein units in the minority group are given greater weights. We demonstrate that the ToM regression adjustment is more robust than Lin 2013's regression adjustment with treatment-covariate interactions, even though these two regression adjustment methods are asymptotically equivalent in completely randomized experiments. Moreover, we extend ToM regression adjustment to stratified randomized experiments, completely randomized survey experiments, and cluster randomized experiments. We obtain design-based properties of the ToM regression-adjusted average treatment effect estimator under such designs. In particular, we show that ToM regression-adjusted estimator improves the asymptotic estimation efficiency compared to the unadjusted estimator even when the regression model is misspecified, and is optimal in the class of linearly adjusted estimators. We also study the asymptotic properties of various heteroscedasticity-robust standard error estimators and provide recommendations for practitioners. Simulation studies and real data analysis demonstrate ToM regression adjustment's superiority over existing methods.

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arXiv2022

Rerandomization and covariate adjustment in split-plot designs

The split-plot design arises from agricultural sciences with experimental units, also known as subplots, nested within groups known as whole plots. It assigns the whole-plot intervention by a cluster randomization at the whole-plot level and assigns the subplot intervention by a stratified randomization at the subplot level. The randomization mechanism guarantees covariate balance on average at both the whole-plot and subplot levels, and ensures consistent inference of the average treatment effects by the Horvitz--Thompson and Hajek estimators. However, covariate imbalance often occurs in finite samples and subjects subsequent inference to possibly large variability and conditional bias. Rerandomization is widely used in the design stage of randomized experiments to improve covariate balance. The existing literature on rerandomization nevertheless focuses on designs with treatments assigned at either the unit or the group level, but not both, leaving the corresponding theory for rerandomization in split-plot designs an open problem. To fill the gap, we propose two strategies for conducting rerandomization in split-plot designs based on the Mahalanobis distance and establish the corresponding design-based theory. We show that rerandomization can improve the asymptotic efficiency of the Horvitz--Thompson and Hajek estimators. Moreover, we propose two covariate adjustment methods in the analysis stage, which can further improve the asymptotic efficiency when combined with rerandomization. The validity and improved efficiency of the proposed methods are demonstrated through numerical studies.

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arXiv2022

Randomization-based joint central limit theorem and efficient covariate adjustment in stratified $2^K$ factorial experiments

Randomized block factorial experiments are widely used in industrial engineering, clinical trials, and social science. Researchers often use a linear model and analysis of covariance to analyze experimental results; however, limited studies have addressed the validity and robustness of the resulting inferences because assumptions for a linear model might not be justified by randomization in randomized block factorial experiments. In this paper, we establish a new finite population joint central limit theorem for usual (unadjusted) factorial effect estimators in randomized block $2^K$ factorial experiments. Our theorem is obtained under a randomization-based inference framework, making use of an extension of the vector form of the Wald--Wolfowitz--Hoeffding theorem for a linear rank statistic. It is robust to model misspecification, numbers of blocks, block sizes, and propensity scores across blocks. To improve the estimation and inference efficiency, we propose four covariate adjustment methods. We show that under mild conditions, the resulting covariate-adjusted factorial effect estimators are consistent, jointly asymptotically normal, and generally more efficient than the unadjusted estimator. In addition, we propose Neyman-type conservative estimators for the asymptotic covariances to facilitate valid inferences. Simulation studies and a clinical trial data analysis demonstrate the benefits of the covariate adjustment methods.

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